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" IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles. "
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... - Page 105
by Euclides - 1858
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The Unfinished Mechanics of Giuseppe Moletti: An Edition and English ...

Giuseppe Moleti, Walter Roy Laird - History - 2000 - 252 pages
...right angle' (Euclid, Elements, 3.31, tr. Heath, 2:61-5). 64 'In any triangle, if one of the sides be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of the triangle are equal to two right angles' (Euclid, Elements, 1.32, tr. Heath, 1:316-22). 65 'If two...
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Philosophy and Geometry: Theoretical and Historical Issues

Lorenzo Magnani - History - 2001 - 284 pages
...universally valid solution of the problem (Kant, 1929, A716-B744, pp. 578-579)." PROP. XXX11. THEOR. 1f a side of any triangle be produced, the exterior angle is equal to the two interiar and oppasite angles ; and the three interior angles af eDery triangle are equal to two right...
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Philosophy and Geometry: Theoretical and Historical Issues

L. Magnani - Gardening - 2001 - 280 pages
...A716-B744, pp. 578-579).13 PROP. XXXII. THEOR. If a side of any triangle be produced, the exterior angle if equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to tico right angles. Let ABC be a triangle, and let one of its sides BC be produced to D ; the...
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The Changing Shape of Geometry: Celebrating a Century of Geometry and ...

Chris Pritchard - Mathematics - 2003 - 572 pages
...exterior angles on the same side equal to two right angles. Prop. 32: In any triangle, if one of the sides be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of the triangle are equal to two right angles. Prop. 38: Triangles which are on equal bases and in the...
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The Cambridge Companion to Kant and Modern Philosophy

Paul Guyer - History - 2006 - 760 pages
...exhibit their concepts in intuition actually to think them. 27. "In any triangle, if one of the sides be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of the triangle are equal to two right angles." Euclid, Elements, p. 316. 28. Because of space limitations,...
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